梁锡坤,陶利民(杭州师范大学 杭州国际服务工程学院 杭州311121)
为完善图像加密的理论及算法体系，并为图像加密实践提供性质优良的可行方案，本文基于Henon映射，构造了一类广义混沌映射—H-S (Henon Sine)映射；并以H-S混沌映射、矩阵非线性变换、矩阵点运算和取整运算为工具，运用序列重排和灰度变换技术设计了一种图像混合加密算法。首先，将第一混沌密钥矩阵和像素矩阵进行非线性变换，通过对变换结果的随机排序，给出了原始图像的置乱加密方法；其次，在置乱图像和第二混沌密钥矩阵之间实施和第一阶段参数不同的变换并应用取整运算实现灰度加密。再次，通过逆运算和逆变换实现图像解密。由于混沌密钥、非线性运算以及随机因素的联合作用，加密算法具有一次一密的的特征，因而具有完备的抗攻击性能；同时算法结构简单、计算复杂度低而便于程序实现；算法规避了常用混沌加密对映射的可逆性要求，对任意大小的矩形图像有效，具有广泛的适用性。加解密仿真实验验证了算法的可行性和有效性，针对加密时间、图像灰度曲面、图像信息熵、加解密图像的相关性和相似性、密钥敏感性、差分攻击等方面展开了全面的加密性能分析，佐证了加密方案的安全性和鲁棒性。同其他类型的置乱加密算法的比对则佐证了算法的优越性。本文算法为任意大小的矩形灰度图像加密提供了参考方案，此方案经过适当调整即可应用于矩形彩色图像加密。
Image Hybrid Encryption Based on A Generalized Chaotic Mapping and Matrix Non-linear Transformation
Image encryption is an important content of digital image processing. It is also one of the basic research fields of applied cryptography. The research of image encryption algorithm not only has the applicable value to the practice of image encryption, but also has the irreplaceable function to promote the cross development of digital image processing method and applied cryptography theory. At present, the research work on image encryption has achieved a lot of important results, but there are still some problems expected to be solved. Firstly, text encryption standards such as DES (Data Encryption Standard), IDEA(International Data Encryption Algorithm), etc need large storage space and have high computational complexity, so these methods cannot be used directly for image encryption. Secondly, some encryption algorithms are oriented to grayscale images. If these algorithms are applied on color images, corresponding algorithm transformation should be performed. Thirdly, some encryption schemes can only be directly applied to square images, such as Arnold transform. For rectangular image encryption, other technology such as image blocking need to be used, which invisibly increases the complexity of the algorithm. In order to improve the algorithm of image encryption, and provide a feasible solution with good properties for image encryption practice, we constructed a generalized chaotic mapping based on Henon chaotic map, which is called H-S (Henon Sine-H-S) mapping. Using H-S map, matrix non-linear transformation, matrices point operation, and rounding operation, an image hybrid encryption algorithm is proposed by means of sequence rearrangement and gray transformation. Firstly, combining the first chaotic key matrix and the original pixels matrix, a nonlinear transformation is conducted by matrix point operation. Using random sorting of the transformation results, the scrambling encryption scheme of the original pixels matrix is given. Secondly, another nonlinear transformation with different parameters is implemented between the scrambled pixels matrix and the second chaotic key matrix, and rounding operation is run to realize gray encryption. Accordingly, the decryption process is carried out using inverse operations and transformations. Due to the combination of chaotic keys, nonlinear operations, and random factors, the algorithm shows the feature of one-time-pad, and demonstrates perfect performance on anti-attacking. Meanwhile, the algorithm has low computational complexity and is convenient for programming. Furthermore, the algorithm circumvents the reversibility requirement of the conventional chaotic encryption for mapping, and can be widely implemented on rectangular images of arbitrary size. The feasibility and effectiveness of the algorithm are shown by the simulation on different sizes of images. A comprehensive encryption performance analysis is carried out for encryption time, image gray surface, image information entropy, correlation and similarity of encryption and decryption images, key sensitivity, and differential attack, which shows the security and robustness of the encryption scheme. In addition, compared with the others scrambling encryption algorithm, the superiority of the algorithm is displayed. The algorithm in this paper provides a reference scheme for the encryption of rectangular gray image of any size. This scheme can be applied to rectangular color image encryption with appropriate adjustment.